1. Field of the Invention
The present invention relates to lenses having refractive index distribution patterns and methods of manufacturing the same.
2. Description of the Prior Art
In optical fiber communication systems, it is important to couple a light source such as a semiconductor laser or a light emitting diode (LED), to a light transmitting medium, such as an optical fiber, as efficiently, as possible. To improve efficiency light from a light source is focused onto the optical fiber using an optical element such as a lens, or the like. Typically, a spherical lens, a cylindrical lens, a focusing rod lens of the gradient refractive index type, or a combination thereof have been used as the optical element.
Among those optical elements, the cylindrical lens is effective to collimate light from a light source and focusing light in only in one direction. This is particularly useful with a semiconductor laser in which the angular range over which light leaves the laser depends on the direction. However, a simple cylindirical lens cannot completely collimate light from the light source because of aberration. Therefore, attempts have been made to improve cylindrical lenses. For example, the applicants of this application have proposed in Japanese patent application No. 16109/1983 a slab-like lens body 10 (see FIG. 1) having a refractive index gradient 12 only along its thickness. That is, as illustrated in FIG. 2, the resulting lens (hereinafter referred to as a slab lens) has a refractive index distribution in which the refractive index n(t), in the direction of thickness (see the left portion of FIG. 2), changes substantially in accordance with the expression EQU n(t).sup.2 =n.sub.o (1-g.sup.2 t.sup.2)
where t represents a half of the thickness of the slab, n.sub.o the refractive index of the slab center, and g the second order constant of the distribution. The right portion of FIG. 2 illustrates that the refractive index is uniform along the directions of length and width. The resulting lens may be placed to provide correction only in the direction in which the radiation angle is large as shown in FIG. 3. This slab lens, however, has a value of g, calculated according to the above-mentioned equation, of approximately g=0.1 mm.sup.-1 with a thickness of 3.6 mm and the numerical aperture NA becomes 0.26-0.30. Accordingly, as shown in FIG. 3, for example, it is difficult to correct a maximum radiation angle of 50 to 60 degrees (NA: 0.77-0.87) of a semiconductor laser 14 when a beam 16 emitted from semiconductor laser 14 is transformed by slab-lens 18 into corrected beam 20. Further, even if a lens is produced by an ordinary ion exchanging method in which a glass plate containing a high refractive index component is immersed in fused salt so as to perform ion-exchanging with respect to the high refractive index ions in the glass plate, it is possible to obtain a high numerical aperture NA=0.5-0.6 and a usual numerical aperture NA=0.35-0.46 in the same manner as in the case of the rod-like lens of the refractive index distribution type. As apparently seen in the embodiment shown in Japanese patent publication No. 37731/1973, the largest refractive index difference in the refractive index distribution is never over 0.08.
In the conventional slab lens, the refractive index may be changed along the thickness, but the numerical aperture is low and the largest refractive index difference is about 0.08.
In order to enlarge refractive index difference, the following method has been proposed. A mask layer is formed on a transparent substrate by photolithography and dopant ions are selectively poured through small bores in the mask layer, thereby producing semispherical lenses of the gradient refractive index distribution. In a planar microlens body obtained through diffusion from surfaces in the manener as described above (hereinafter referred to as a surface diffusion method), the refractive index difference between the central portion and the circumferential portion becomes large, and is about 0.2, but the numerical aperture of the lens, when the lens is used alone, is when the lens is used alone.
Further, Japanese patent application Laid-Open No. 106503/1983, discloses a technique where a mask layer 22 is provided with an opening slit portion 24 having a predetermined shape formed on a transparent substrate 26 as shown in FIG. 4. Ions are diffused through opening 24 so as to form a semicylindrical lens portion corresponding to a gradient refractive index distribution 28 which is used as a unidirectional refractive index distribution type lens, similar to a cylindrical lens. In this case, however, there has been a problem in that the numerical apertures is only about 0.3 at largest.
Also, as electronic copying machines have become reduced in size, a rod lens array 30 (see FIG. 5) including a number of rod type light condensing lenses 32 have been used as an imaging optical system. Rod type light condensing lenses 32 are obtained by pouring a solution of dopant into apertures of, for example, a porous glass body. A portion of the dopant is then removed from the glass body to form a density gradient in the dopant distribution in the aperture. The glass body is dried and then subject to baking to thereby crush the apertures (Japanese patent application Laid-Open No. 12607/1976).
Each of light condensing lenses 32 has a refractive index distribution which decreases in a radial direction gradually in proportion to the square of the distance from a rod central axis 34 (see FIG. 6). The lens length Z.sub.O is from 1/2 to 3/4 of the distance in which the light within the lens system produces the erect real image of an object as shown in FIG. 7.
In order to form a lens array by using a rod type light condensing lenses 32, the lenses are stacked two of three deep as shown in FIG. 8, aligned in one direction, and sandwiched between upper and lower plates 36. Each rod type light condensing lens 32 has an imaging (focusing) conjugate length T (see FIG. 7) defined as the sum of the distance S.sub.1, between one end surface of lens 32 and an object 38, the distance S.sub.2 between the other end of lens 32 and an erect real image 40, and the length Z.sub.O of lens 32. The conjugate length T depends on the value of g, representing a quadratic constant of the distribution when the numerical aperture NA of the lens or the refractive index distribution of the lens is approximated as follows: EQU n(r).sup.2 =n.sub.o.sup.2 (1-g.sup.2 r.sup.2)
where
n.sub.o represents the refractive index on the central axis of a rod type glass body, and PA1 n(r) represents the refractive index at the position of the radius r from the central axis. There is an advantage in that as the numerical aperture or the value of g becomes larger the conjugate length T can be made shorter and hence the device can be made more compact.
Further, a lens array is known in which semicylindrical lens portions are formed in transparent substrates. That is, in Japanese patent application Laid-Open No. 106503/1983 and as shown in FIG. 9, a transparent substrate 42a having a plurality of semicylindrical lens portions 44a whose center axes are parallel with each other, and another transparent substrate 42b of the same form having similar semicylindrical lens portions 44b, are put together such that the respective flat surfaces of the semi-cylindrical portions are arranged face to face and the respective axes of the lens portions of the two substrates are perpendicular to each other, so that a very small lens assembly body 46 is obtained with an optical axis which extends along the z axis in the direction perpendicular to each of the semi-cylindrical lens portions of the two substrates.
A problem exists with a rod lens array as shown in FIG. 5 in that when cylindrical lenses 32 are piled in a staggered relationship, a large number of lenses must be bundled with axes 34 parallel to each other with a required degree of accuracy, and further sandwiched or pressed by plates.
As a result, construction is difficult and time consuming. The array obtained according to the above-mentioned Japanese patent application Laid-Open No. 106503/1983 is of the two-dimensional surface type and a problem exists in that the optical axis is perpendicular to each of the axes of the semi-cylindrical lens portions of the two substrates so that a large numerical aperture cannot be obtained.